This paper describes a simplified model of an electric circuit with a DC-DC converter and a PID-regulator as a system of integral differential equations with an identically singular matrix multiplying the higher derivative of the desired vector-function. We use theoretical results on integral and differential equations and their systems to prove solvability of such a model and analyze its stability.

翻译：本文描述了一种带有 DC-DC 转换器和 PID 调节器的简化电路模型，该模型被表述为一个积分-微分方程组，其特点是乘以期望向量函数高阶导数的矩阵恒为奇异矩阵。我们利用积分方程、微分方程及其系统的理论结果，证明了此类模型的可解性，并分析了其稳定性。